论文标题
与测量数据的线性和准线性椭圆问题的加权p-拉普拉斯近似
Weighted p--Laplace approximation of linear and quasi-linear elliptic problems with measure data
论文作者
论文摘要
我们将解决方案近似于一些线性和退化的准线性问题，该问题涉及右侧和异质性各向异性型号的偏式差异矩阵，涉及线性椭圆运算符（如richards和stefan方程的半差异）。通过添加加权p-拉普拉斯项获得了此近似值。 R和（-1，1）之间选择的差异性很好，用于近似溶液的估计，并参与上述重量。我们表明，在右侧右侧位于L 1中的情况下，这种近似值将一般右侧的问题和熵解决方案收敛。
We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side and heterogeneous anisotropic diffusion matrix. This approximation is obtained through the addition of a weighted p--Laplace term. A well chosen diffeomorphism between R and (--1, 1) is used for the estimates of the approximated solution, and is involved in the above weight. We show that this approximation converges to a weak sense of the problem for general right-hand-side, and to the entropy solution in the case where the right-hand-side is in L 1 .
